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Asked by jain.pradeep | 16th Feb, 2020, 08:29: PM

Expert Answer:

Let the circular ring attached to rod rotates with frquency f ,
Since different parts of rod are moving with different speed, we have,  EMF induced in rod = begin mathsize 14px style integral subscript 0 superscript l v space B space d s end style
where v is linear speed of a small length ds of rod which is at a distance s from centre .
 
B is uniform magnetic flux density
 
linear speed v is related to frequency as,  v = (2πf) s
 
Hence EMF induced in the rod = begin mathsize 14px style integral subscript 0 superscript l left parenthesis 2 pi f space s space right parenthesis space B space d s space equals space left parenthesis 2 pi B space f space right parenthesis space integral subscript 0 superscript l space s space d s space equals space pi space l squared B space f end style
Current in the rod = EMF / resistance = ( π l2 B f ) / R
 
Force on rod = ( B i l ) = ( π l3 B2 f ) / R

Answered by Thiyagarajan K | 17th Feb, 2020, 04:37: PM

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